Except for being exact opposites, and that white holes are really just a mathematical theory to balance out black holes, like Neo and Agent Smith.

There is more to it than that, it is believed space-time is curved and the gravitational distortion in the fabric of space-time is so strong it is believed that it punches a hole in it and thus the idea of a white hole, because the matter has to go somewhere. Whether or not that is accurate remains to be seen, but they have found that black holes can evaporate.